"They can't do it, because when they come home that's when they put Australians at risk" said Morrison during the press conference.
He also said "Sunday barbeques" should be cancelled but added that Australians should exercise their "common sense" on what social contact with friends and family is acceptable.
A new COVID-19 text messaging campaign, announced by the government on Wednesday, caused further consternation after the first message failed to include the most recent advice to stay home unless "absolutely necessary". "I'm not going to do that lightly", he said.
"We have been making the point for some time".
I had hoped that would have been fully complied with and I've got to say, Australians have been pretty good about it.
"If we do all these things, then we are going to be able to put greater pressure on slowing the rate of the spread of this virus", Mr Morrison told reporters in Canberra.
Non-urgent elective surgeries in Australia's public and private hospitals will be banned from midnight in a bid to preserve the healthcare system to respond to the coronaviruspandemic.
"It's going to be a tough year in 2020 and one of the things I don't want to have yielded up is a year of a child's education, which is so important".
Mr Morrison said some states would be considering criminal penalties for people who hold large house parties. "Where possible the National Cabinet together is going to try and keep Australia functioning in a way that continues to support jobs and activity in our economy which is not going to compromise the health advice that we're receiving".
Boris Johnson Orders Three-Week Nationwide Lockdown
Everyone from the supermarket staff to the transport workers to the carers to the nurses and doctors on the frontline. Shopping for " basic necessities", as infrequently as possible. "And use food delivery services where you can ".